## anonymous one year ago Solve these inequalities. (ii) 3^x +5 bigger or equal to 32 Please help! I don't know how to solve this though I a aware it involves logarithms. Please show me what to do and explain why.

1. Nnesha

$\huge\rm 3^x +5 \ge 32$ yes right you have to take log both sides but first move 5 to the right side and then take log

2. Nnesha

make sense ?

3. anonymous

So It would be $3^{x} \ge 17$ ? How do I take log of both sides?

4. Nnesha

17 ?? i guess thats a typo

5. anonymous

Um no actually. What did I do wrong?

6. Nnesha

how did you get 17 ?

7. anonymous

I subtracted 5 from both sides?

8. Nnesha

yes right so 32-5 isn't equal to 17 :=)

9. anonymous

Ooooh. I do mistakes like that often. Oops!

10. anonymous

ok so after $3^{x} \ge 27$ how do I take log of both sides?

11. Nnesha

yes right now take log both sides and apply the product rule $\huge\rm log (3)^x \ge \log(27)$

12. Nnesha

power rule ***

13. anonymous

Ok I am new too logarithms so sorry for taking so much time. If you use the power rule does that mean that I move the exponent x in front of the first logarithm?

14. Nnesha

yes right :=) and its okay take ur time!

15. anonymous

Thanks! All right so, $x \log_{}3 \ge \log27$

16. Nnesha

yes right now to solve for x you should move log(3) to the right side :=) and then use calculator :P that's it!

17. anonymous

Ok, thank you so much! :D

18. Nnesha

what did you get ?? o.O

19. anonymous

x$x \ge 3$

20. Nnesha

yes right!

21. Nnesha

good job!

22. anonymous

Hooray!